Brain tumor visualization for magnetic resonance images using modified shape-based interpolation method

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 12, No. 3, June 2022, pp. 2553~2563
ISSN: 2088-8708, DOI: 10.11591/ijece.v12i3.pp2553-2563  2553
Journal homepage: http://ijece.iaescore.com
Brain tumor visualization for magnetic resonance images using
modified shape-based interpolation method
Dina Mohammed Sherif El-Torky1
, Mohamed Ismail Roushdy2
, Maryam Nabil Al-Berry1
,
Mohammed Abd El-Megeed Salem3
1
Faculty of Computer and Information Sciences, Ain Shams University, Cairo, Egypt
2
Faculty of Computers and Information Technology, Future University in Egypt, Cairo, Egypt
3
Faculty of Media Engineering and Technology, German University in Cairo, Cairo, Egypt
Article Info ABSTRACT
Article history:
Received Dec 18, 2020
Revised Dec 28, 2021
Accepted Jan 10, 2022
3D visualization plays an essential role in medical diagnosis and setting
treatment plans especially for brain cancer. There have been many attempts
for brain tumor reconstruction and visualization using various techniques.
However, this problem is still considered unsolved as more accurate results
are needed in this critical field. In this paper, a sequence of 2D slices of
brain magnetic resonance Images was used to reconstruct a 3D model for the
brain tumor. The images were automatically segmented using wavelet
multi-resolution expectation maximization algorithm. Then, the inter-slice
gaps were interpolated using the proposed modified shape-based
interpolation method. The method involves three main steps; transferring the
binary tumor images to distance images using a suitable distance function,
interpolating the distance images using cubic spline interpolation and
thresholding the interpolated values to get the reconstructed slices. The final
tumor is then visualized as a 3D isosurface. We evaluated the proposed
method by removing an original slice from the input images and
interpolating it, the results outperform the original shape-based interpolation
method by an average of 3% reaching 99% of accuracy for some slice
images.
Keywords:
Brain tumors
Magnetic resonance images
Shape-based interpolation
Visualization
This is an open access article under the CC BY-SA license.
Corresponding Author:
Dina Mohammed Sherif El-Torky
Faculty of Computer and Information Sciences, Ain Shams University
Al-Khalifa Al-Maamoun St., Abbassiya, Cairo, Egypt
Email: dina.eltorky@cis.asu.edu.eg
1. INTRODUCTION
Brain cancer is one of the most life-threatening diseases to human beings. More than 22,000 people
in the United States of America are diagnosed with brain tumors every year [1]. The treatment process
involves one or more of surgical resection, radiotherapy, and chemotherapy. For the oncologist to decide a
suitable treatment plan, there must be an accurate and reliable diagnosis of the pathology, location, shape,
and size of the tumor. The diagnostic techniques are mainly divided into invasive techniques, e.g., biopsy,
and non-invasive techniques such as medical imaging tools.
Magnetic resonance imaging (MRI) is an important imaging tool for medical diagnosis especially
for lesions. The images can show the lesion properties when injecting the patient with Gadolinium-based
contrast agent [2]. However, the MRI yields a set of cross-sectional 2D images that need further
interpretation from an expert radiologist to construct a 3D model of the tumor from these slices. This can
result in an inaccurate diagnosis because the analysis depends on the experience of the radiologist [3]–[5].
Moreover, to avoid the slices from interference with each other (crosstalk artifacts), there must be an inter-

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Int J Elec & Comp Eng, Vol. 12, No. 3, June 2022: 2553-2563
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slice spacing during the image acquisition [6] which causes loss of details in the gap spaces and extra effort
from the radiologist to analyse the images.
As a result, many attempts are being made to provide an automated visualization for brain tumors.
We propose a modified shape-based interpolation technique to estimate the missing information in the gap
slices then reconstruct a 3D model of the tumor that can be easily viewed and interpreted. First, the tumor is
segmented from each MRI slice. Then the tumor images are converted to distance images which are used to
interpolate the in-between missing slices. Finally, the tumor volume is rendered and displayed in a 3-D view.
The rest of the paper is organized; section 2 reviews the most popular methods that are currently
used for tumor 3D reconstruction. Section 3 explains the methods used for tumor segmentation and
extraction. The proposed method is presented in section 4. Results are shown in section 5 and the conclusions
are demonstrated in section 6.
2. RELATED WORK
3D reconstruction is implemented using various methods that are based on diverse concepts. In this
section, we will discuss the most widely-used methods [3].
2.1. Delaunay and alpha-shapes
Delaunay methods are mainly based on extracting tetrahedron surfaces from an initial point cloud.
The concept of 3D reconstruction using alpha-shapes was first introduced by Edelsbrunner and Mucke [7].
Using a finite set of points S and the parameter alpha, the resulting alpha-shape of S is a polytope, which is a
generalization in any number of dimensions, of the three-dimensional polyhedron that is not necessarily
convex or connected. If the alpha value is large, the alpha shape of S is similar to its convex hull. By
decreasing the value of alpha, the non-convex details of the shape are formed. Edelsbrunner and Mucke [7]
modified the technique by forming a surrounding sphere smaller than alpha then removing all tetrahedrons
that lie inside it. External triangles of the remaining tetrahedron form the final surface. Al-Tamimi et al. [8]
used alpha-shape theory for 3D reconstruction of brain tumors using slices of MR images. Most
delaunay-based methods have the advantage of accurately fitting the surface defined by the original point
cloud. On the other hand, their performance is strongly affected with noise.
2.2. Zero-set methods
Zero-set methods are also known as implicit reconstruction methods. They use a distance function
for surface reconstruction. A polygonal representation of the object is formed by extracting a zero-set using a
contour algorithm. Therefore, surface reconstruction from a point cloud is simplified to computing the
suitable function f which equals zero for the sampled points and does not equal zero for the rest of the
points [3]. The most popular zero-set method is the marching cubes algorithm which was proposed by
Lorensen and Cline [9]. Guo et al. [10] introduced an improved marching cube algorithm by combining the
seeded region growing and the standard Monte Carlo (MC) algorithm. Many other methods were proposed
based on Zero-set methods such as Kazhdan and Hoppe [11] and Walder et al. [12] The drawback of these
methods is the loss of geometrical accuracy in high-curvature areas such as corners and edges of the re-
constructed shape.
2.3. Point-based methods
From the popular point-based methods is the voxel-grid filtering. It is based on the idea of reducing
the number of points by sampling the input space using a grid of 3D voxels then a centroid is selected for
each voxel to represent all the points [13], [14]. Angelopoulou et al. [15] used growing neural models to
automatically landmark the target volume sections and construct a 3D model. The shortcoming of these
methods is that it is impossible to determine the final number of points representing the surface. Methods that
depend on deep learning and neural networks as in [16] and [15] were also proposed. Although that these
methods produce highly efficient output, they have a drawback of finding the suitable training data especially
with brain tumors that have various shapes, sizes, and consistencies.
2.4. Interpolation-based methods
To avoid interfering of slices during MRI acquisition (crosstalk artifact), there must be a gap
between the images. The interpolation-based methods idea is based on calculating the image values in the
gap area to reconstruct the 3D model accurately. These methods can be divided into scene-based and
object-based methods. The simplest scene-based method is the linear interpolation. More methods were then
proposed such as cubic spline and other polynomials in interpolation of medical images [17]. The kriging
method was also used to interpolate grey values of medical images [18]. The scene-based methods apply

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Brain tumor visualization for magnetic resonance images using … (Dina Mohammed Sherif El-Torky)
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intensity averaging on the neighboring slices without considering the shape feature distortion. This causes
blurriness to the object boundaries of the resulting interpolated slices.
Several object-based interpolation methods were proposed to avoid the shortcomings of the
scene-based methods. They considered object information in the given input slices to guide the interpolation
procedure. An efficient type of object-based methods is the shape-based interpolation [19], this method uses
distance transform functions to build distance images from the given slices. Then, instead of interpolating the
intensity values, it interpolates the displacement preserving the geometric changes of the objects more
accurately. The shape-based methods have become widely used due to their efficiency. Yet, they have the
problem of disability to effectively deal with object having holes, large offsets, or heavy invagination.
In [20], multi-resolution registration was used for image interpolation. Farias et al. [21] used
interpolation techniques to generate intermediate slices of medical images. Ting et al. [2] applied surface
reconstruction using Hermite surface interpolation for breast cancer. Our proposed method uses shape-based
interpolation to estimate the intermediate gap slices of the brain tumor volume.
3. PROPOSED METHOD
Our system is based on two main processes: tumor segmentation of brain MR images and
intermediate slices interpolation of binary tumor images. Various segmentation methods have been proposed
throughout the past years. These methods could be very simple such as Thresholding, or region-based as
region growing and watershed, or supervised classification as in artificial neural networks, or statistical-based
such as expectation maximization and its modifications [22]–[26]. We used wavelet multi-resolution
expectation maximization algorithm (WMEM) [27] proposed by Salem [28], [29] for tumor segmentation.
Besides being an unsupervised method, WMEM showed very accurate segmentation results for the brain MR
images. Figure 1 shows the process flow diagram of the proposed method.
Figure 1. Process flow diagram of the proposed method
3.1. Multiresolution-based segmentation
The WMEM is basically a modification of the classic expectation maximization (EM) algorithm.
The EM consists of two major steps: expectation step (E-step) and maximization step (M-step). These two
steps are repeated until convergence, i.e., the difference between the parameters in the previous and the
current iterations decreases until it reaches a given threshold. The EM then uses a classifier that assigns a
class membership to a pixel 𝑖 depending on its intensity 𝑥𝑖. The class to which the pixel is assigned is the one
having a parameter vector that maximizes the Gaussian density function. The WMEM uses a Haar wavelet
transform function that produces four outputs: image approximation, and vertical, horizontal and diagonal
details of the image [30]–[32]. Two levels of approximations were produced to form a parent and a

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grandparent of the original image. Since the edge details are lost during formation of the parent and
grandparent images, these pixels are usually misclassified.
To overcome this, a mask containing all the edges of the image is formed by adding the vertical,
horizontal and diagonal details images resulted from the wavelet analysis. This mask is used to exclude the
pixels laying on the edges of the image from multi-resolution segmentation. The original EM is applied on
each of the original, parent and grandparent images. Each classification result is given a certain weight. Then,
the final classification is calculated by combining the three weighted results as:
𝐶(𝑥,𝑦) = 0.4 ∗ 𝐶0(𝑥,𝑦) + 0.35 ∗ 𝐶1(𝑥,𝑦) + 0.25 ∗ 𝐶2(𝑥,𝑦)
where, 𝐶0, 𝐶1 and 𝐶2 are the results of the classification at pixel (𝑥, 𝑦) for the original, parent and
grandparent images respectively. Figure 2 shows the segmentation results of the WMEM, Figure 2(a) the
original tumor image, Figure 2(b) the original segmented image using EM, Figure 2(c) the segmented parent
image, Figure 2(d) the segmented grandparent image, Figure 2(e) the final segmented image using WMEM,
and Figure 2(f) the extracted tumor.
(a) (b) (c)
(d) (e) (f)
Figure 2. Stages of tumor extraction: (a) the original tumor image, (b) the original segmented image using
EM, (c) the segmented parent image, (d) the segmented grandparent image, (e) the final segmented image
using WMEM, and (f) the extracted tumor
3.2. Tumor extraction
Thresholding was used to separate the other segmented brain components (grey matter, white
matter, and CSF) from the tumor. The thresholding produced images containing both tumor and skull
because they almost have the same color intensity. So, the solidity feature was used to exclude the skull from
the final image. Solidity is the proportion of the pixels in the convex hull that are also in the region. It is
computed as Area/ConvexArea. It was found that tumors have higher solidity than the skull, so we selected
the high solidity to get a binary image that only contains the tumor to be used in the reconstruction step [27].
3.3. Intermediate slice estimation
Our aim is to visualize the brain tumor given a series of MRI brain slices. Our method is a
modification of the classic shape-based interpolation technique [33] which is based on interpolating the
values of the 3D volume that lay in the gap areas during slices acquisition. Shape-based interpolation is
performed in two main steps. The first step is transforming the binary tumor image into a distance image. The
second step is interpolating the distance image using a suitable interpolation function.
Every series of MRI image is described with some important information such as the slice thickness,
inter-slice distance and the in-plane resolution. These properties vary according to the MRI scanner strength
and acquisition process. Before starting the interpolation, the number of gap slices should be calculated using
the provided dataset properties. We computed the gap area in pixels by:

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𝑠𝑙𝑖𝑐𝑒 𝑠𝑝𝑎𝑐𝑖𝑛𝑔
𝑖𝑛 − 𝑝𝑙𝑎𝑛𝑒 𝑟𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
where, slice spacing is the gap between every two consecutive slices in millimeters and the in-plane
resolution is the area of each pixel in millimeters [34].
3.4. Distance image transform
The distance image represents the shortest distance from every pixel in the image to the nearest
boundary pixel. Pixels inside the region of interest (tumor) are assigned with positive values, while pixels of
the background are assigned with negative values. We calculated the distance transform by applying the
following steps twice for each of the tumor and the background separately, then the two distance images are
added to form the final distance image.
Steps:
Step 1: Create two distance images 𝐷 and 𝐷′for the tumor and the background respectively, then set all the
pixels of 𝐷 and 𝐷′ to zero.
Step 2: Create a counter 𝐼 that increments with every iteration.
Step 3: Starting from the boundary pixels, perform an erosion operation to the image to remove a single pixel
from the tumor boundaries then add the value of 𝐼 to the pixels of 𝐷 at the locations of the eroded
pixels.
Step 4: Repeat step 3 until all the pixels of 𝐷 are calculated.
Step 5: Similarly, perform dilation to the tumor image by adding a single pixel starting from the boundary
pixels and subtract the value of 𝐼 in each iteration and insert its value in 𝐷′ at the locations of the
dilated pixels.
Step 6: Repeat step 5 until all the values of 𝐷′ are calculated.
Step 7: By adding 𝐷 to 𝐷′, the final distance image is formed.
The previous steps are performed for every slice of the input volume. Figure 3 shows a sample of
the distance image that results from applying the previous steps on one of our dataset images, the in-lined
part represents the tumor area with positive values, while the outlined negative pixels represent the
background and the zero pixels are for the tumor boundaries.
Figure 3. A sample of the resulting distance image
3.5. Slice interpolation
To reconstruct the final tumor volume, the gap area has to be interpolated using the given slices.
Several interpolation methods have been used in medical imaging. Methods such as nearest neighbour and
linear interpolation are fast and simple, yet they do not produce reliable results [35]. In our work, B-spline
interpolation [36] was used on distance images as an input, and it proved to show accurate results.
A separable spline model is chosen for interpolation. The p-dimensional spline function
𝑠(𝑋), 𝑋 = (𝑥1, … , 𝑥𝑝) ∈ 𝑅𝑝
is represented by the expansion
𝑠(𝑋) = ∑ 𝑐(𝑘)𝜑(𝑋 − 𝑘)
𝑘∈𝑍𝑝 (1)

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where, 𝑐(𝑘) are the B-spline coefficients. The basis functions in (1) are the integer shifts of the separable B-
spline 𝜑(𝑋), which is a tensor product of the univariate B-splines of degree n:
𝜑(𝑋) = 𝛽𝑛(𝑥1) … 𝛽𝑛
(𝑥𝑝) (2)
From the fold convolution of the box function, we can obtain the univariate B-splines. Their closed form
expression is:
𝛽𝑛(𝑥) =
∆𝑛+1𝑥+
𝑛
𝑛!
(3)
where, 𝑥+
𝑛
= max{0, 𝑥}𝑛
is the one-sided power function and ∆𝑛+1
is the (𝑛 + 1) iteration of the central
finite difference operator ∆𝑓(𝑥) = 𝑓 (𝑥 +
1
2
) − 𝑓(𝑥 −
1
2
). For a multidimensional image array 𝑓(𝑖),𝑖 ∈ 𝑍𝑝
,
the basic interpolation problem is to determine the coefficients c(k) in (1) such that the spline 𝑆(𝑋) fits the
pixel values exactly: 𝑆(𝑋)|𝑥=𝑖 = 𝑓(𝑖), 𝑖 ∈ 𝑍𝑝
. By applying this constraint and resampling (1) at the integers
we get:
𝑓(𝑖) = ∑ 𝑐(𝑘)𝜑(𝑖 − 𝑘).
𝑘∈𝑍𝑝 (4)
Since (4) has the form of discrete convolution, we can determine the 𝑐(𝑘) values by deconvolving the
equation. In this study, experimental results showed that cubic spline interpolation proved to have higher
accuracy than many interpolation methods such as linear, cubic and Hermite-splines.
3.6. Interpolated slice binarization
After applying interpolation on the input distance images of the tumor slices, the resulting
interpolated distance images must be converted to binary images so that the gap slices can be inserted
accurately. That was simply done be assigning all the zero and positive values to one (representing the tumor
area) and zero to all the negative values (representing the background). By analyzing the results of
shape-based interpolation, it was found that the interpolated image is always smaller than the ground truth
image (i.e., the majority of error is produced as false negative pixels). This happens due to assigning all the
interpolated negative values as background pixels, even if their value is very small. To overcome this
drawback, we added a thresholding step to approximate the negative values so that they are not considered as
background. The threshold was selected upon experimental trials. This modification improved the accuracy
of the original method for all the used dataset images.
3.7. Visualization
After interpolating all the intermediate slices for the whole tumor images, the original and
interpolated slices are stacked to form a 3D volume. Then, Isosurface is extracted and displayed in a
3-dimensional view. Figure 4 shows the visualized brain tumor before slices interpolation, while Figure 5
shows the visualized tumor using slices interpolation. It is noticed that the details of the tumor shape are
displayed clearly after applying the proposed method.
Figure 4. Displayed tumor volume without interpolation

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Figure 5. The displayed interpolated tumor volume
4. RESULTS AND DISCUSSION
Data from the Internet brain segmentation repository (IBSR) was used in this study [37] which is
provided by the Center for Morphometric Analysis at Massachusetts General Hospital. The data consists of
multiple brain MRI scans for a patient with a tumor taken at roughly 6-month intervals over three and a half
years. The algorithm was implemented using MATLAB® R2017b. Table 1 demonstrates the properties of
the used MRI images series.
As the provided data does not contain ground truth values, the system accuracy was calculated by
removing an original slice from the MRI images, then interpolating it. The interpolated image was then
compared with the original removed image and the percent error was computed as (5):
𝛿 =
|𝑂𝐴−𝐼𝐴|
𝑂𝐴
× 100 (5)
where, OA is the area of the object cross section in the removed slice and IA is the area of the object cross
section in the interpolated slice. We compared our method with the original shape-based interpolation
proposed by Raya and Udupa [33] and with Hermite interpolation used in [2].
The results are summarized in Tables 2 to 5. The results represent the accuracy percentage for each
slice which is computed as 100 − 𝛿, where 𝛿 is the error percentage mentioned in (5). The first and last
slices were excluded from the computations because for reliable interpolation results, the query points should
lie in between the control points [33].
Table 1. Properties of the used MRI images series
Series no. No. of slices with tumor Slice Spacing (mm) In-plane Resolution
126_10 17 3 1.015625
126_13 16 2.5 1.015625
126_21 17 2.5 0.937500
126_26 17 0 0.937500
Table 2. Accuracy percentage for each interpolated slice for series 126_10 of IBSR dataset
Slice no. Original shape-based Hermite interp. Modified shape-based interp.
2 83.8 88.2 92.1
3 84.0 91.2 92.7
4 85.8 86.6 91.6
5 86.3 88.3 91.9
6 90.0 92.4 95.0
7 87.9 91.5 93.4
8 90.8 92.2 94.6
9 86.6 89.2 94.5
10 88.1 91.1 93.9
11 88.4 91.3 95.7
12 88.2 89.6 94.8
13 86.6 88.0 92.0
14 85.5 90.4 93.6
15 83.9 91.1 94.9
16 83.5 92.7 95.2

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2 79.2 81.4 86.7
3 80.1 90.6 91.6
4 81.3 88.0 92.3
5 86.5 92.1 94.1
6 87.0 92.1 94.3
7 88.7 92.1 94.6
8 88.8 94.9 96.0
9 87.7 91.0 95.8
10 88.7 95.0 96.1
11 88.6 90.7 94.7
12 89.7 94.8 96.8
13 87.6 89.8 92.9
14 81.4 83.2 90.0
15 79.1 84.6 89.9
mean ±variance 85.31±16.53 90.02±18.50 93.27±8.382
2 83.3 87.6 92.4
3 83.0 85.5 91.6
4 84.7 87.6 92.1
5 86.3 91.9 92.6
6 92.3 94.5 96.0
7 92.8 96.2 97.1
8 90.9 93.9 96.2
9 92.4 93.0 95.9
10 89.6 90.5 93.8
11 90.0 89.5 92.8
12 91.7 95.6 97.4
13 88.6 88.9 95.9
14 92.1 95.9 97.0
15 89.2 91.5 93.9
16 81.7 85.8 89.7
mean ±variance 88.57±14.556 91.19±13.19 94.29±5.629
Table 5 Accuracy percentage for each interpolated slice for series 126_26 of IBSR dataset
2 83.4 88.9 92.2
3 89.4 90.7 93.9
4 90.4 91.4 94.5
5 91.3 92.0 95.6
6 89.8 92.3 95.8
7 89.6 93.7 95.6
8 87.9 91.4 94.9
9 92.9 94.2 97.1
10 93.0 95.2 97.7
11 92.2 93.8 96.7
12 92.8 93.6 96.1
13 90.5 93.4 95.8
14 91.4 93.2 95.9
15 90.6 93.1 96.3
16 85.7 89.9 92.7
mean ±variance 90.06±7.248 92.45±2.987 95.38±2.33
The final accuracy of the interpolated tumor volume is expected to be higher than the accuracy of
the previous results. As when removing an original slice, the distance between the given slices (i.e., control
points) is doubled, which will eventually decrease the interpolation accuracy. It was also noticed in Figure 6
that the error pixels are distributed evenly around the tumor boundary, Figure 6(a) the original tumor image,
Figure 6(b) the interpolated tumor image, and Figure 6(c) the difference between A and B, green pixels
represent the false positives and red pixels represent the false negatives. We used the structural similarity
index (SSIM) to compare the interpolated and the original images. SSIM tells how much one image is
structurally similar to the other [38], [39]. Values between 98% and 99% were gained. This shows that the
interpolated tumor preserved its original shape and curvature areas, which will not affect the medical analysis
of the system output. Since no automatic method has yet been proved to be reliable for usage as ground truth,

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human expertise is still needed to confirm the efficiency of the automatic methods [40]. We contacted some
experts in the Neurosurgical department of Ain Shams University, and they approved the reliability and
efficiency of the reconstructed tumor images.
(a) (b) (c)
Figure 6. Difference between original and interpolated tumor images, (a) the original tumor image,
(b) the interpolated tumor image, and (c) the difference between a and b, green pixels represent the false
positives and red pixels represent the false negatives
5. CONCLUSION
Brain tumor visualization can efficiently help in treatment planning and resection assessment of
brain cancer. Having accurate information about the shape and size of the tumor will increase the chances of
total resection, which will eventually increase the mean survival period of the patient. Many attempts have
been done for brain tumor visualization using different methods such as alpha-shapes, marching cubes, point-
based methods, and interpolation-based methods.
In this paper, we presented a modified shape-based interpolation method for 3D reconstruction of
brain tumors using a group of parallel MRI image slices. The tumor was first segmented from each brain
slice using the WMEM algorithm, then the gap area was computed using our method. The final 3D shape of
tumor was then displayed using isosurface function. The accuracy of the system was calculated by removing
an original slice from the series and interpolating it, then comparing both images. An average accuracy of
94.1% was gained when comparing the images pixel by pixel, while the average SSIM was 98.5% which
reveals that the proposed method preserves the structural shape of the interpolated slices.
ACKNOWLEDGEMENTS
We would like to thank the Neurosurgery Department in Faculty of Medicine, Ain Shams
University for providing us with expert feedback for our results.
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BIOGRAPHIES OF AUTHORS
Dina Mohammed Sherif El-Torky is an Assistant Lecturer in basic sciences
department and PhD student at Faculty of Computer and Information Sciences, Ain Shams
University. She is specialized in medical image processing. She can be contacted at email:
dina.eltorky@cis.asu.edu.eg. A list of her research activity can be found at:
https://www.researchgate.net/profile/Dina_Eltorky
Mohamed Ismail Roushdy he is a Professor of Computer Science and Dean of
Faculty of Computers and Information Technology, Future University in Egypt, Cairo,
Egypt. He is also the Former Dean of Faculty of Computer and Information Sciences,
Ain Shams University, Cairo, Egypt. He can be contacted at email:
Mohamed.Roushdy@fue.edu.eg. A list of his research publications can be found at:
https://www.researchgate.net/profile/Mohamed_Roushdy3
Maryam Nabil Al-Berry is an Assistant Professor at Scientific Computer
Department, Faculty of Computer and Information Sciences, Ain Shams University. She is
specialized in Machine Learning, Image Processing and Computing in Mathematics. She can
be contacted at email: maryam_nabil@cis.asu.edu.eg. More about her bibliography is listed
in https://www.researchgate.net/profile/Maryam_Al-berry
Mohammed Abd El-Megeed Salem an Associate Professor at both Faculty of
Media Engineering and Technology, German University in Cairo and Faculty of Computer
and Information Sciences, Ain Shams University. He is specialized in Computing in
Mathematics, Natural Science and Artificial Intelligence. He can be contacted at email:
salem@cis.asu.edu.eg. He has more than one hundred research items that can be viewed at
https://www.researchgate.net/profile/Mohammed_Abdel-Megeed_Mohammed_Salem

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